Average Error: 40.0 → 0.3
Time: 2.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (((double) exp(x)) - 1.0)) / x));
}

↓
double code(double x) {
	double VAR;
	if ((x <= -0.0001557085886761992)) {
		VAR = ((double) (((double) (((double) cbrt(((double) (((double) pow(((double) exp(x)), 3.0)) - ((double) pow(1.0, 3.0)))))) * ((double) cbrt(((double) (((double) pow(((double) exp(x)), 3.0)) - ((double) pow(1.0, 3.0)))))))) / ((double) (((double) (x / ((double) cbrt(((double) (((double) pow(((double) exp(x)), 3.0)) - ((double) pow(1.0, 3.0)))))))) * ((double) (((double) pow(((double) exp(x)), 2.0)) + ((double) (1.0 * ((double) (((double) exp(x)) + 1.0))))))))));
	} else {
		VAR = ((double) (1.0 + ((double) (x * ((double) (0.5 + ((double) (x * 0.16666666666666666))))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original40.0
Target40.5
Herbie0.3
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  x  < -1.5570858867619921e-4
    1. Initial program 0.1
      \[\]
    2. Using strategy rm
    3. Applied flip3--0.1
      \[\leadsto \]
    4. Applied associate-/l/0.1
      \[\leadsto \]
    5. Simplified0.1
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-cube-cbrt0.1
      \[\leadsto \]
    8. Applied associate-/l*0.1
      \[\leadsto \]
    9. Simplified0.1
      \[\leadsto \]
    if -1.5570858867619921e-4 <  x 
    1. Initial program 60.1
      \[\]
    2. Taylor expanded around 0 0.4
      \[\leadsto \]
    3. Simplified0.4
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "Kahan's exp quotient"
  :precision binary64

  :herbie-target
  (if (and (< x 1.0) (> x -1.0)) (/ (- (exp x) 1.0) (log (exp x))) (/ (- (exp x) 1.0) x))

  (/ (- (exp x) 1.0) x))